They are now 15 points behind Serie A leaders, Napoli.
Lecce managed ten shots on goal, however only one was on target.
Inter’s lead came in the 29th minute after a Barella square pass in the box was met by Mkhitaryan whose one-touch finish sent the ball into the top right corner.
The home side were dominant with 63 per cent possession and doubled their lead in the 53rd minute.
Arturo Martinez scored an eerily similar goal, finishing off another square pass – this time from Dumfries - without needing to take a touch.
Lecce remain nine points above the relegation zone.
